Finite Group Databasebeta

← #13079727

Subgroups — #13079727

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623065C211yesmaximal, characteristic, complemented
2#10623057C211yesmaximal, characteristic, complemented
3C11×#433C211yesmaximal, characteristic, complemented
4#10622462C211yesmaximal, characteristic, complemented
5#10622458C211yesmaximal, characteristic, complemented
6#10622457C211yesmaximal, characteristic, complemented
7#10622454C211yesmaximal, characteristic, complemented
8#10622352C211yesmaximal, characteristic, complemented
9#10622351C211yesmaximal, characteristic, complemented
10#10622347C211yesmaximal, characteristic
11#10622346C211yesmaximal, characteristic, complemented
12#10622328C211yesmaximal, characteristic, complemented
13#10622327C211yesmaximal, characteristic, complemented
14#10622309C211yesmaximal, characteristic, complemented
15#10622294C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C11×#117C2211yescharacteristic
19#66983C2211yescharacteristic
20#66977C2211yescharacteristic
21C2×Dic44C2211yescharacteristic
22C2×Dic44C2211yescharacteristic
23C2×Dic44C2211yescharacteristic
24C2×D88C2211yescharacteristic
25C2×#4314C2211yescharacteristic
26C2×#4314C2211yescharacteristic
27C2×#4314C2211yescharacteristic
28C2×#4314C2211yescharacteristic
29#66951—21no—
30#66950—21no—
31#66950—21no—
32#66949—21no—
33#66939—21no—
34#66939—21no—
35#66938—21no—
36#66936—21no—
37#66928C2211yescharacteristic
38#66928C2211yescharacteristic
39#66928C2211yescharacteristic
40C4×D44C2211yescharacteristic
41#66922C2211yescharacteristic
42#66922C2211yescharacteristic
43#66922C2211yescharacteristic
44C4×Dic22C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47C11×C22⋊C8C2211yescharacteristic
48C11×C22⋊C8C2211yescharacteristic
49C11×#97C2211yescharacteristic
50C4×C8×C11C2211yescharacteristic
51#66885C2211yescharacteristic
52#66885C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C2×C22⋊D11—21no—
61C2×C22⋊D11—21no—
62C22×Dic11—21no—
63#4339—41no—
64#4339—41no—
65C2×D44C2311yescharacteristic
66C2×D44C2311yescharacteristic
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22—41no—
72C2×Dic22—41no—
73C2×Dic22C2311yescharacteristic
74C2×Dic22C2311yescharacteristic
75C2×Dic22C2311yescharacteristic
76C2×Dic22C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4D411yescharacteristic
82C11×C4⋊C4D411yescharacteristic
83C11×C22⋊C4D411yescharacteristic
84C11×C22⋊C4D411yescharacteristic
85C42×C11C2311yescharacteristic
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11C2311yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105C4×Dic11—21no—
106Dic44—41no—
107Dic44—41no—
108Dic44—41no—
109D88—41no—
110#4314—41no—
111#4314—41no—
112#4314—41no—
113#4314—41no—
114#3225—111nomaximal, Sylow
115C23×C11C2×D411yescharacteristic
116C22×D11—21no—
117C22×D11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C22⋊D11—42no—
127C22⋊D11—81no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—42no—
135D44—21no—
136D44—21no—
137D44—21no—
138D44—21no—
139C4×D11—42no—
140C4×D11—81no—
141Dic22—21no—
142Dic22—21no—
143Dic22—21no—
144Dic22—21no—
145Dic22—21no—
146Dic22—21no—
147Dic22—21no—
148Dic22—21no—
149Dic22—42no—
150Dic22—81no—
151C8×C11—21no—
152C8×C11—21no—
153C8×C11—21no—
154C8×C11—21no—
155#542—111no—
156#536—111no—
157#497—111no—
158#495—111no—
159#489—111no—
160#487—111no—
161#464—111no—
162#463—111no—
163#462—111no—
164#461—111no—
165#452—111no—
166#451—111no—
167#449—111no—
168#448—111no—
169#433D1111yescharacteristic, complemented
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11C22×D411yescharacteristic
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11H(5,𝔽2)11yescharacteristic
186C4×C11H(5,𝔽2)11yescharacteristic
187Dic11—41no—
188Dic11—41no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C22×Q8—111no—
195C2×Q16—111no—
196C2×Q16—111no—
197C2×Q16—111no—
198C2×SD16—111no—
199C2×SD16—111no—
200C2×SD16—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C4⋊Q8—111no—
204C4⋊Q8—111no—
205C4⋊Q8—111no—
206#126—221no—
207#124—111no—
208#124—111no—
209#124—111no—
210#124—221no—
211#123—221no—
212#123—221no—
213#123—221no—
214C22⋊Q8—111no—
215C22⋊Q8—221no—
216C22⋊Q8—221no—
217C22⋊Q8—221no—
218#121—111no—
219C4×Q8—111no—
220C4×D4—111no—
221#117C2×D1111yescharacteristic
222C4⋊C8C2×D1111yescharacteristic
223C4⋊C8C2×D1111yescharacteristic
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#103—111no—
229#103—111no—
230#102—111no—
231#102—111no—
232C22⋊C8C2×D1111yescharacteristic
233C22⋊C8C2×D1111yescharacteristic
234#97C2×D1111yescharacteristic
235C4×C8C2×D1111yescharacteristic
236C2×C11—41no—
237C2×C11#53511yescharacteristic
238C2×C11#57711yescharacteristic
239C2×C11#57811yescharacteristic
240D11—81no—
241D11—81no—
242#41—441no—
243#41—441no—
244C2×Q8—111no—
245C2×Q8—111no—
246C2×Q8—111no—
247C2×Q8—111no—
248C2×Q8—221no—
249C2×Q8—221no—
250C2×Q8—441no—
251C2×Q8—441no—
252C2×D4—111no—
253C2×D4—111no—
254C2×D4—221no—
255C2×D4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4C22×D1111yescharacteristic
260Q16—441no—
261Q16—441no—
262Q16—441no—
263SD16—441no—
264SD16—441no—
265SD16—441no—
266SD16—441no—
267D8—441no—
268C2×C8C22×D1111yescharacteristic
269C2×C8C22×D1111yescharacteristic
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4D4411yescharacteristic
282C4⋊C4D4411yescharacteristic
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4D4411yescharacteristic
293C22⋊C4D4411yescharacteristic
294C42—221no—
295C42C22×D1111yescharacteristic
296C42C22×D1111yescharacteristic
297C11#322511yescharacteristic, complemented, Sylow
298C23—221no—
299C23—221no—
300C23C2×D4411yescharacteristic
301Q8—221no—
302Q8—221no—
303Q8—221no—
304Q8—221no—
305Q8—221no—
306Q8—221no—
307Q8—221no—
308Q8—221no—
309Q8—442no—
310Q8—881no—
311D4—221no—
312D4—221no—
313D4—221no—
314D4—221no—
315D4—442no—
316D4—881no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—881no—
328C2×C4C2×D4411yescharacteristic
329C2×C4C2×D4411yescharacteristic
330C2×C4C2×D4411yescharacteristic
331C2×C4C2×D4411yescharacteristic
332C2×C4C2×D4411yescharacteristic
333C2×C4C23×D1111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—441no—
342C22—441no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22C22×D4411yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—441no—
354C4—441no—
355C4—441no—
356C4—441no—
357C4—441no—
358C4—441no—
359C4#6704211yescharacteristic
360C4#6704211yescharacteristic
361C2—41no—
362C2—881no—
363C2—881no—
364C2#1062305611yescharacteristic
365C2#1062328211yescharacteristic
366C2#1062328411yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#433C2
socleC22×C11C22×D4
prime radical#10622347C2
hypercenter#433D11
hypocenterC11#3225
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10623065C2semidirect
2. #10623057C2semidirect
3. C11×#433C2semidirect
4. #10622462C2semidirect
5. #10622458C2semidirect
6. #10622457C2semidirect
7. #10622454C2semidirect
8. #10622352C2semidirect
9. #10622351C2semidirect
11. #10622346C2semidirect
12. #10622328C2semidirect
13. #10622327C2semidirect
14. #10622309C2semidirect
15. #10622294C2semidirect
169. #433D11semidirect
297. C11#3225semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106230652
#106230572
C11×#4332
#106224622
#106224582
#106224572
#106224542
#106223522
#106223512
#106223472
#106223462
#106223282
#106223272
#106223092
#106222942
#322511